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STRUCTURE OF TITANIUM ISOTOPES
By Prof. Lefteris Kaliambos (Natural Philosopher in New Energy) (August 2014) Unfortunately the discovery of the assumed uncharged neutron (1932) along with the invalid relativity (EXPERIMENTS REJECT RELATIVITY) led to the abandonment of the well-established electromagnetic laws, in favor of various contradicting nuclear theories which could not lead to the nuclear structure. Under this physics crisis in 2003 I published my paper “structure is governed by the fundamental laws of electromagnetis Nuclear structure is governed by the fundamental laws of electromagnetism ” by reviving the natural laws which led to my discovery of 288 quarks in nucleons including 9 charged quarks in proton and 12 ones in neutron able to give considerable charge distributions in nucleons for discovering the nuclear force and structure by applying the laws of electromagnetism (See my papers of nuclear structure in FUNDAMENTAL PHYSICS CONCEPTS ). Naturally occurring titanium (Ti) is composed of 5 stable isotopes; Ti-46, Ti-47, Ti-48, Ti-49 and Ti-50 with Ti-48 being the most abundant (73.8% natural abundance). Twenty-one radioisotopes have been characterized, with the most stable being Ti-44 with a half-life of 60 years, Ti-45 with a half-life of 184.8 minutes, Ti-51 with a half-life of 5.76 minutes, and Ti-52 with a half-life of 1.7 minutes. All of the remaining radioactive isotopes have half-lives that are less than 33 seconds and the majority of these have half-lives that are less than half a second. The least stable is Ti-61, but it has a half-life somewhat longer than 300 nanoseconds. WHY Ti-46, Ti-47, Ti-48, Ti-49 AND Ti-50 ARE STABLE NUCLIDES After a careful analysis of the structure of atomic nuclei I discovered that the beta decay is due to the fact that in unstable nuclei there exist single horizontal pn bonds of weak binding energy leading to the beta decay. For example in my paper STRUCTURE AND BINDING OF H3 AND He3 using the diagram of the structure of the H3 one sees that it is unstable because the two neutrons make single np bonds, while the He3 is stable because the one neutron between the two protons makes two np bonds per neutron. On the other hand the pp repulsions of long range lead to the instability when we have a small number of pn bonds per nucleon. In my papers STRUCTURE OF Ti-44 Sc-44 AND Ca-44 and STRUCTURE OF Sc-45 AND Ti-45 and also STRUCTURE OF Ti-48 AND V-48 we explained carefully why the Ti-44 with S=0 , and the Ti-45 with S =-7/2 are unstable nuclides and why the Ti-48 with S=0 is a stable nuclide. However for understanding the stable structure of such nuclides we use the following diagrams of Ti-46 and Ti-47. In the diagram Ti-46 with S=0 you see that the extra n23(-1/2) of -HP6 and n24(+1/2) of +HP1 are responsible for the stability of Ti-46 because they make two bonds per neutron able to give enough energy to bonds for overcoming the pp and nn repulsions. In this structure the core is the parallelepiped of Mg-24 with S=0 in which the 4 alpha particles existing from p13 to n20 give also S=0 . Here you see that the deuteron p21n21 of +HP5 gives S=+1 while the deuteron p22n22 of -HP2 gives S =-1. In other words it has S=0 with two extra neutrons giving two bonds per neutron. Similarly the Ti-50 has extra neutrons with two bonds per neutron able to overcome the pp and nn repulsions. NUCLEAR STRUCTURE OF Ti-52, Ti-54, Ti -56, Ti-58, Ti-60 AND Ti-62 WITH S=0 After a careful analysis we found that the unstable structure of the above nuclides is based on the structure of Ti-46. For example the Ti-62 with S=0 has 16 more extra neutrons of opposite spins than those of Ti-46 giving single bonds unable to overcome the nn repulsions of short range. NUCLEAR STRUCTURE OF Ti-44, Ti-42, Ti-40, AND Ti-38 WITH S=0 Similarly the structure of the above nuclides is based on the structure of Ti-46 with S=0. For example in the absence of 8 neutrons of opposite spins we get the structure of Ti-38 with S=0. ' ' STRUCTURE OF STABLE Ti-46 WITH S = 0 This structure consists of 6 horizontal planes of opposite spins like the +HP1, -HP2, +HP3, -HP4, +HP5 and –HP6. The nucleons n17, p17, p18, and n18, of the alpha particle with S=0 existing in front of p5, n5, n7 and p7 respectively are not shown here. Similarly the nucleons p19, n19, n20 and p20 of the'' alpha particle with S=0 existing behind the n6, p6, p8, and n8 respectively are not shown here. Note that the extra n23(-1/2) and n24(+1/2) with two bonds per neutron lead to the stability of Ti-46 with S=0 ' ' ' p12..........n12''' ' -HP6 n11..........p11.........n23 ' ' n10..........p10..........n21' ' +HP5 p9............n9..........p21 ' ' n14..........p8............n8............p16' ' -HP4 p14..........n7............p7...........n16 ' ' p13..........n6............p6............n15' ' +HP3 n13..........p5...........n5............p15 ' ' n22.........p4............n4' ' -HP2 p22..........n3............p3 ' ' n2............p2' ' +HP1 n24..........p1...........n1 ' However for understanding the stable structure of Ti-47 and Ti-49 we present the following diagram of Ti-47 with S = -5/2 . In this diagram you see that the core is the parallelepiped of Mg-24 with S=0 having 4 alpha particles (from p13 to n20 with S=0 ) like the structure of calcium. Here the two alpha particles existing in front and behind the parallelepiped are not shown. Also the three extra neutrons like the n23(-1/2) the n24(+1/2) and the n25(-1/2) are not shown because the n23 is behind the p16 and the n24 and n25 are in front of p3 and p9 respectively. Note that they fill blank positions for making two bonds per neutron able to lead to the stability of Ti-47 with S =-5/2. Since the deuterons p21n21 and p22n22 of -HP2 give S = -2, we conclude that the total spin is given by S = 0 +0 -1/2 +1/2 -1/2 -2 = -5/2 Also the stable structure of Ti-49 with S=-7/2 is due to the fact that the blank positions formed by the alpha particles are able to receive two more extra neutrons of opposite spins giving two bonds per neutron able to overcome the nn repulsions of short range. ' ' NUCLEAR STRUCTURE OF Ti-51, Ti-53, Ti-55, Ti-57, Ti-59, Ti-61 AND Ti-63 After a careful analysis we found that the unstable structure of the above nuclides is based on the structure of T-47 with S=-5/2. For example the Ti-63 with S=-1/2 has 4 extra neutrons of negative spins and 12 extra neutrons of opposite spins giving S=0. That is S = -5/2 + 4(-1/2) + 0 = -1/2 . NUCLEAR STRUCTURE OF Ti-43, Ti-41 AND Ti-39 Similarly the structure of Ti-43 with S=-7/2 is based on the structure of Ti-47 with 5= -5/2 . In this case, in the absence of two neutrons of positive spins and in the absence of two neutrons of opposite spins giving S=0 we get the structure of Ti-43 with S= -7/2. That is S = -5/2 -2(+1/2) -0 = -7/2 However the structures of Ti-41 and Ti-39 with S =+3/2 are based on a new structure similar to the structure of Ti-47. In these two cases all nucleons change the spins of Ti-47 and we have a new Ti-47 with S =+5/2. For example we have -HP1, +HP2, -HP3, +HP4 -HP5 and +HP6 giving S = + 5/2. Therefore in the absence of two neutrons with positive spins and of 4 neutrons of opposite spins giving S=0 we get the structure of Ti-41 with S=+3/2. That is S = +5/2 - 2(+1/2) - 0 = +3/2. Similarly in the absence of two neutrons of opposite spins of the structure of Ti-41 with S=+3/2 we get the structure of Ti-39 with S =+3/2. ' ' DIAGRAM OF Ti-47 WITH S =-5/2 The core of this structure is the parallelepiped of Mg-24 with S=0 consisting of six horizontal planes with opposite spins like the +HP1, -HP2, +HP3, -HP4, +HP5 and the -HP6. Here the nucleons from p17 to n20 forming the two alpha particles existing in front and behind the parallelepiped along with the 3 extra neutrons of blank positions are not shown. ' ' ' p12..........n12' ' -HP6 n11..........p11.........n23 ' ' n10..........p10' ' +HP5 p9............n9 ' ' n14..........p8............n8............p16' ' -HP4 p14..........n7............p7...........n16 ' ' p13..........n6............p6............n15' ' +HP3 n13..........p5...........n5............p15 ' ' n21.........p4............n4...........p22' ' -HP2 p21..........n3............p3...........n22 ' ' n2............p2' ' +HP1 p1...........n1 ' ' ' ' ' Category:Fundamental physics concepts